1 2 3 zvzv xvxv yvyv 4 5 67 7 8 9 1011 12 Only one face of an object
These two planes are called the near- far clipping planes, or the front-back clipping planes. The near and far planes allow us to exclude objects that are in front of or behind the part of the scene that we want to display.
Axonometric Orthogonal Projection We can also form orthogonal projections that display more than one face of an object. Such views are called axonometric orthogonal projections. The most commonly used axonometric projection is the isometric projection, which is generated by aligning the projection plane (or the object) so that the plane intersects each coordinate axis in which the object is defined, called the principal axes.
7-7 Oblique Parallel Projections In general, a parallel-projection view of a scene is obtained by transferring object descriptions to the view plane along projection paths that can be in any selected direction relative to the view-plane normal vector. When the projection path is not perpendicular to the view plane, this mapping is called an oblique parallel projection.
7-8 Perspective Projections We can approximate this geometric- optics effect by projecting objects to the view plane along converging paths to a position called the projection reference point (or center of projection).
Perspective projection z-axis vanishing point y z x
fig 6.3 One-point perspective projections of a cube onto a plane cutting the z axis showing vanishing point of lines perpendicular to projection plane [Foley et al.] One-Point Perspective Projection
2-Point Perspective Projections 1) Rotate object with an angle about y- axis 2) Translate object by [0 m n] 3) Perform 1-point perspective projection onto the xy-plane (z=0)
3-Point Perspective Projections 1) Rotate object with an angle about y- axis 2) Rotate object with an angle about x- axis 3) Translate object by [0 m n] 4) Perform 1-point perspective projection onto the xy-plane (z=0)